As a vigil was held for a two-time Iraq war veteran whose skull was fractured allegedly during a clash between protesters and Oakland police, Wednesday night's Occupy protests could be a bellwether on whether police have agitated or suppressed the movement, analysts said.

"The police chose to make the situation more contentious. Now the question is whether they were right in their calculation," said Michael Heaney, assistant professor of organizational studies and political science at the University of Michigan.

"Have they suppressed the movement or have they galvanized it?" Heaney said.

Already, the Oakland violence has prompted a warning from police in New York that they will pursue legal action against any protesters who injure police officers. Separately, the Atlanta mayor accused the movement of becoming violent and ordered arrests late Tuesday night.

Olsen, a member of Iraq Veterans Against the War, was in serious but stable condition Wednesday afternoon at Highland General Hospital in Oakland, said Dottie Guy, a member of the veterans group who told CNN by phone that she was visiting Olsen at the hospital.

He sustained a skull fracture after allegedly being struck in the head with a police projectile, according to the veterans group. Among a growing number of war vets participating in the Occupy movement, Olsen was marching from a downtown library toward City Hall in an effort to reclaim an encampment that had been cleared out by police, the veterans group said.

The violence between police and protesters escalated after demonstrators allegedly pelted officers with bottles, rocks and paint, authorities said. Police then fired tear gas into the downtown streets to disperse the crowd.

That exchange was preceded by police ordering the dismantling of a tent camp set up by Occupy protesters in a park in front of City Hall.

Also Tuesday evening, Atlanta police arrested demonstrators at a downtown park. "This movement is moving toward escalation. That it is no longer peaceful in my judgment and there are elements in that movement that are willing to engage in violence," Atlanta Mayor Kasim Reed said. "So I'm not going to let that stand."

Meanwhile, the Sergeants Benevolent Association of the New York City Police Department warned Wednesday that it will pursue legal claims against any Occupy Wall Street protesters who injure any of its members.

So far, more than 20 New York City officers have been injured in Occupy-related incidents, said Ed Mullins, president of the association.

"In light of the growing violence attendant to the Occupy movements across the country, particularly as evidenced by the recent events in Oakland, I am compelled to place these so-called 'occupiers' on notice that physical assaults on police officers will not be tolerated," Mullins said in a statement.

"I am deeply concerned that protesters will be emboldened by the recent rash of violent acts against police officers in other cities. New York's police officers are working around the clock, as the already-overburdened economy in New York is being drained by 'occupiers' who intentionally and maliciously instigate needless and violent confrontations with the police," Mullins said.

The Oakland violence marks a controversial turn in the Occupy movement, which began in mid-September in New York's Wall Street district and has since mushroomed to dozens of cities across the country.

The national movement has no leader and is denouncing the widespread gap between the rich and, according to the movement's slogan, "the remaining 99%" of the country.

"I think part of it is that the movement is largely leaderless," Sherry Bebitch Jeffe, a senior fellow at the University of Southern California's School of Policy, Planning and Development, said about the Oakland clash.

"If someone is frustrated, there's no guarantee that they are going to channel it into something positive or if they're going to channel it in something negative," Jeffe said.

Heaney said the Oakland police action -- closing down the encampment -- may have been a mistake.

"One of the things that I've been impressed with the Occupy movement is there hasn't been any violence" against people or property, Heaney said. "It's impressive because the people at the heart of this movement are self-identified anarchists. The Occupy movement is organized by anarchist principles of decentralized movement."

Until this week, the movement had been disciplined -- then the Oakland police eliminated the encampment outside City Hall, Heaney said.

"People are going to respond to that in a not-peaceful way," Heaney said. "Either they (law enforcement officials) expected that this would be the response or they were incompetent not to expect this response.

"When you engage in (more than) 100 unjustifiable arrests, basically what you do is give credibility to the people you're trying to stop," Heaney said. "The smarter strategy on the part of police is to ignore them and it would eventually burn out and people would go home."

Oakland police said about 300 protesters were gathered in Frank Ogawa Plaza, the park in front of City Hall, and began throwing rocks and bottles at officers about 10 p.m. Tuesday after police told the demonstrators to disperse.

Police then used "less-than-lethal munitions including tear gas," authorities said.

Then, between 4 a.m. and 4:30 a.m. Wednesday, a small group of protesters made several unsuccessful attempts to enter the park, and police used force again to thwart them, authorities said.